Attack range is the maximum distance between an attacker and his/her target. Attack range varies from weapon to weapon.
Melee attacks have the shortest attack range. You can only attack people who are 1 block away (right next to you) unless you are holding a halberd, in witch it is 2 blocks away.
Range and Magic attacks have a very long attack range. In the attack style tab in Runescape, you can choose the Long Range attack style. This style gives you the maximum attack speed. Any other style will give you a slightly shorter range. Most pures do not use long ranged while PKing because it gains defense exp and the attacks are slightly slower.
Lots of players use halberds to attack enemies that they could die from. This is a popular choice in the Tzhaar caves, as the monsters there are high level and most of them can only use melee.